def main(): # Initialize PAOFLOW, indicating the name of the QE save directory. # outputdir is named 'output' by default # smearing is 'gauss' by default paoflow = PAOFLOW.PAOFLOW(savedir='silicon.save', outputdir='output', smearing='gauss', npool=1, verbose=True) paoflow.read_atomic_proj_QE() paoflow.projectability() paoflow.pao_hamiltonian() # Calculate eigenvalues on the default ibrav=2 path paoflow.bands(ibrav=2, nk=2000) # Dimension of the grid is doubled by default # e.g. 12x12x12 -> 24x24x24 paoflow.interpolated_hamiltonian() # Calculate eigenvalues on the entire BZ grid paoflow.pao_eigh() paoflow.gradient_and_momenta() paoflow.adaptive_smearing() paoflow.dos(emin=-12., emax=2.2, ne=1000) paoflow.transport(emin=-12., emax=2.2) paoflow.finish_execution()
def main():
label = 'sym'
outdir = 'output_%s' % label
savedir = 'silicon_%s.save' % label
# Initialize PAOFLOW, indicating the name of the QE save directory.
paoflow = PAOFLOW.PAOFLOW(savedir=savedir,
outputdir=outdir,
smearing='gauss',
npool=1,
verbose=True)
paoflow.projectability()
paoflow.pao_hamiltonian()
# Calculate eigenvalues on the default ibrav=2 path
paoflow.bands(ibrav=2, nk=2000)
# Dimension of the grid is doubled by default
# e.g. 12x12x12 -> 24x24x24
paoflow.interpolated_hamiltonian()
# Calculate eigenvalues on the entire BZ grid
paoflow.pao_eigh()
paoflow.gradient_and_momenta()
# Dump PAOFLOW data for future runs.
paoflow.restart_dump(fname_prefix='paoflow_dump')
paoflow.finish_execution()
def main():
paoflow = PAOFLOW.PAOFLOW(savedir='MoP2.save',
verbose=False,
outputdir="./output")
paoflow.read_atomic_proj_QE()
paoflow.projectability(pthr=0.95)
paoflow.pao_hamiltonian(symmetrize=True, thresh=1.e-10, max_iter=64)
paoflow.z2_pack()
paoflow.find_weyl_points(search_grid=[8, 8, 8])
paoflow.finish_execution()
def main():
model = {'label':'simple_cubic', 't':1.0}
paoflow = PAOFLOW.PAOFLOW(model=model, outputdir='./simple_cubic', verbose=True)
path = 'G-X-M-G-R'
special_points = {'G':[0.0, 0.0, 0.0],'X':[0.0, 0.5, 0.0],'M':[0.5, 0.5, 0.0],'R':[0.5,0.5,0.5]}
paoflow.bands(ibrav=1, nk=100, band_path=path, high_sym_points=special_points)
paoflow.finish_execution()
def main():
paoflow = PAOFLOW.PAOFLOW(savedir='pt.save', smearing='m-p')
paoflow.projectability()
paoflow.pao_hamiltonian()
paoflow.interpolated_hamiltonian()
paoflow.pao_eigh()
paoflow.gradient_and_momenta()
paoflow.adaptive_smearing()
paoflow.dos(emin=-8., emax=4., delta=.2)
paoflow.transport(emin=-8., emax=4., t_tensor=[[0, 0]])
paoflow.dielectric_tensor(metal=True, emin=.5, emax=10., d_tensor=[[0, 0]])
paoflow.finish_execution()
def main():
paoflow = PAOFLOW.PAOFLOW(savedir='al.save')
paoflow.projectability(pthr=.97)
paoflow.pao_hamiltonian()
paoflow.interpolated_hamiltonian()
paoflow.pao_eigh()
paoflow.gradient_and_momenta()
paoflow.adaptive_smearing()
paoflow.dos(do_pdos=False, delta=.1, emin=-12., emax=3.)
paoflow.transport(emin=-12., emax=3., t_tensor=[[0, 0]])
paoflow.dielectric_tensor(metal=True, emin=.05, emax=6., d_tensor=[[0, 0]])
paoflow.finish_execution()
def main():
paoflow = PAOFLOW.PAOFLOW(savedir='al.save', verbose=True)
paoflow.read_atomic_proj_QE()
paoflow.projectability(pthr=.97)
paoflow.pao_hamiltonian()
paoflow.interpolated_hamiltonian()
paoflow.pao_eigh()
paoflow.gradient_and_momenta()
paoflow.adaptive_smearing()
paoflow.dos(do_pdos=False, delta=.1, emin=-12., emax=3.)
paoflow.transport(emin=-12., emax=3.)
paoflow.finish_execution()
def main():
paoflow = PAOFLOW.PAOFLOW(savedir='pt.save', smearing='m-p')
paoflow.read_atomic_proj_QE()
paoflow.projectability()
paoflow.pao_hamiltonian()
paoflow.bands(ibrav=2)
paoflow.interpolated_hamiltonian()
paoflow.pao_eigh()
paoflow.gradient_and_momenta()
paoflow.adaptive_smearing()
paoflow.dos(emin=-8., emax=4., delta=.2)
paoflow.transport(emin=-8., emax=4.)
paoflow.finish_execution()
def main(): paoflow = PAOFLOW.PAOFLOW(savedir='./fe.save') paoflow.projectability(pthr=0.95) paoflow.pao_hamiltonian() paoflow.bands(ibrav=3, nk=2000) paoflow.topology(spol=2, ipol=1, jpol=2, eff_mass=True, Berry=True) paoflow.interpolated_hamiltonian() paoflow.pao_eigh() paoflow.gradient_and_momenta() paoflow.adaptive_smearing() paoflow.dos(do_pdos=False) paoflow.anomalous_Hall(do_ac=True, emin=-8., emax=4., a_tensor=np.array([[0,1]])) paoflow.finish_execution()
def main():
# Initialize PAOFLOW as a 'restart' run
paoflow = PAOFLOW.PAOFLOW(restart=True)
# Load the dumped data using the same file prefix
paoflow.restart_load(fname_prefix='paoflow_dump')
# Continue calculations
paoflow.adaptive_smearing()
paoflow.dos(emin=-12., emax=2.2, ne=1000)
paoflow.transport(emin=-12., emax=2.2, t_tensor=[[0, 0]])
paoflow.dielectric_tensor(emax=6., d_tensor=[[0, 0]])
paoflow.finish_execution()
def main():
paoflow = PAOFLOW.PAOFLOW(savedir='al.save', npool=8)
paoflow.projectability(pthr=.97)
paoflow.pao_hamiltonian(non_ortho=True)
paoflow.add_external_fields()
paoflow.bands(ibrav=2, nk=2000)
paoflow.interpolated_hamiltonian()
paoflow.pao_eigh()
paoflow.gradient_and_momenta()
paoflow.adaptive_smearing()
paoflow.dos(do_pdos=False, emin=-12., emax=3.)
paoflow.transport(emin=-12., emax=3., t_tensor=[[0, 0]])
paoflow.dielectric_tensor(metal=True, emin=.05, emax=6., d_tensor=[[0, 0]])
paoflow.finish_execution()
def main(): paoflow = PAOFLOW.PAOFLOW(savedir='pt.save') paoflow.read_atomic_proj_QE() paoflow.projectability() paoflow.pao_hamiltonian() paoflow.bands(ibrav=2, nk=2000) paoflow.topology(Berry=True, eff_mass=True, spin_Hall=True, spol=2, ipol=0, jpol=1) paoflow.interpolated_hamiltonian() paoflow.pao_eigh() paoflow.gradient_and_momenta() paoflow.adaptive_smearing() paoflow.dos(do_pdos=False, emin=-8., emax=4.) paoflow.spin_Hall(emin=-8., emax=4., s_tensor=[[0,1,2]]) paoflow.finish_execution()
def main():
paoflow = PAOFLOW.PAOFLOW(savedir='silicon.save',
smearing='gauss',
npool=1,
verbose=True)
paoflow.projectability()
paoflow.pao_hamiltonian()
paoflow.bands(ibrav=2, nk=2000)
paoflow.interpolated_hamiltonian()
paoflow.pao_eigh()
paoflow.gradient_and_momenta()
paoflow.adaptive_smearing()
paoflow.dos(emin=-12., emax=2.2)
paoflow.transport(emin=-12., emax=2.2, t_tensor=[[0, 0]])
paoflow.dielectric_tensor(emax=6., d_tensor=[[0, 0]])
paoflow.finish_execution()
def main():
paoflow = PAOFLOW.PAOFLOW(savedir='./pt.save')
arry, attr = paoflow.data_controller.data_dicts()
paoflow.read_atomic_proj_QE()
paoflow.projectability()
paoflow.pao_hamiltonian()
paoflow.adhoc_spin_orbit(
phi=0.0,
theta=0.0,
naw=np.array([9]), # number of orbitals for each atom
lambda_p=np.array([0.0]), # p orbitals SOC strengh for each atom
lambda_d=np.array([0.5534]), # d orbitals SOC strengh for each atom
orb_pseudo=['spd']) # type of pseudo potential for each atom
path = 'gG-X-W-K-gG-L-U-W-L-K|U-X'
special_points = {
'gG': (0.0, 0.0, 0.0),
'K': (0.375, 0.375, 0.750),
'L': (0.5, 0.5, 0.5),
'U': (0.625, 0.250, 0.625),
'W': (0.5, 0.25, 0.75),
'X': (0.5, 0.0, 0.5)
}
paoflow.bands(ibrav=2,
nk=1000,
band_path=path,
high_sym_points=special_points)
paoflow.topology(Berry=True,
eff_mass=True,
spin_Hall=True,
spol=2,
ipol=0,
jpol=1)
paoflow.interpolated_hamiltonian()
paoflow.pao_eigh()
paoflow.gradient_and_momenta()
paoflow.adaptive_smearing()
paoflow.dos(do_pdos=False, emin=-8., emax=4.)
paoflow.spin_Hall(emin=-8., emax=4., s_tensor=[[0, 1, 2]])
paoflow.finish_execution()
def main():
model = {'label': 'Kane_Mele', 't': 1.0, 'soc_par': 0.1, 'alat': 1.0}
paoflow = PAOFLOW.PAOFLOW(model=model,
outputdir='./kane_mele',
verbose=True)
path = 'G-M-K-G'
special_points = {
'G': [0.0, 0.0, 0.0],
'K': [2.0 / 3.0, 1.0 / 3.0, 0.0],
'M': [1.0 / 2.0, 0.0 / 2.0, 0.0]
}
paoflow.bands(ibrav=4,
nk=100,
band_path=path,
high_sym_points=special_points)
paoflow.finish_execution()
def main():
model = {'label': 'graphene', 't': 2.7}
paoflow = PAOFLOW.PAOFLOW(model=model,
outputdir='./graphene',
verbose=True)
path = 'G-M-K-G'
special_points = {
'G': [0.0, 0.0, 0.0],
'K': [2.0 / 3.0, 1.0 / 3.0, 0.0],
'M': [1.0 / 2.0, 0.0 / 2.0, 0.0]
}
paoflow.bands(ibrav=4,
nk=100,
band_path=path,
high_sym_points=special_points)
paoflow.finish_execution()
def main():
paoflow = PAOFLOW.PAOFLOW(savedir='alp.save')
paoflow.projectability()
paoflow.pao_hamiltonian()
correction_Hubbard = np.zeros(32, dtype=float)
correction_Hubbard[1:4] = .1
correction_Hubbard[17:20] = 2.31
paoflow.add_external_fields(HubbardU=correction_Hubbard)
paoflow.bands(ibrav=2, nk=2000)
paoflow.interpolated_hamiltonian(nfft1=24, nfft2=24, nfft3=24)
paoflow.pao_eigh()
paoflow.gradient_and_momenta()
paoflow.adaptive_smearing()
paoflow.dos(do_pdos=False, emin=-8., emax=5., delta=.1)
paoflow.transport(emin=-8., emax=5., t_tensor=[[0, 0]])
paoflow.dielectric_tensor(emax=6., d_tensor=[[0, 0]])
paoflow.finish_execution()
def main():
paoflow = PAOFLOW.PAOFLOW(savedir='SnTe.save', npool=4, verbose=1)
paoflow.read_atomic_proj_QE()
paoflow.projectability(pthr=0.90)
# Smearing is specified in QE for convergence, force PAOFLOW to treat it as an insulator
paoflow.pao_hamiltonian(insulator=True)
# Define high symmetry points and the path comprised of such points
# '-' defines a continuous transition to the next high symmetry point
# '|' defines a discontinuous break in from one high symmetry point to the next
path = 'G-X-S-Y-G'
special_points = {
'G': [0.0, 0.0, 0.0],
'S': [0.5, 0.5, 0.0],
'X': [0.5, 0.0, 0.0],
'Y': [0.0, 0.5, 0.0]
}
paoflow.bands(ibrav=8,
nk=1000,
band_path=path,
high_sym_points=special_points)
paoflow.interpolated_hamiltonian(nfft1=140, nfft2=140, nfft3=1)
paoflow.pao_eigh()
paoflow.spin_operator()
paoflow.fermi_surface(fermi_up=0.0, fermi_dw=-1.)
paoflow.spin_texture(fermi_up=0.0, fermi_dw=-1.)
paoflow.gradient_and_momenta()
paoflow.adaptive_smearing()
paoflow.spin_Hall(twoD=True,
emin=-3.5,
emax=1.5,
s_tensor=[[0, 1, 2], [1, 0, 2]])
paoflow.finish_execution()
def main():
# Start PAOFLOW, interpolate Hamiltonian, compute gradient an momenta
paoflow = PAOFLOW.PAOFLOW(savedir='GaAs.save', smearing=None, npool=1, verbose=True)
arrays,attr = paoflow.data_controller.data_dicts()
paoflow.read_atomic_proj_QE()
paoflow.projectability()
paoflow.pao_hamiltonian()
paoflow.interpolated_hamiltonian(nfft1=40, nfft2=40, nfft3=40)
paoflow.pao_eigh()
paoflow.gradient_and_momenta()
# Compute the chemical potential at specified doping concentration for various temperatures
doping = -3.5e17
paoflow.doping(tmin=380, tmax=812, nt=28, emin=-36, emax=2, ne=5000, doping_conc=doping)
# Define the functional form for our 'custom' TauModel
me = 9.10938e-31 # Electron Mass
ev2j = 1.60217662e-19 # Electron Charge
def acoustic_model ( temp, eigs, params ):
# Formula from Fiorentini paper on Mg3Sb2, DOI: 10.1088/1361-648X/aaf364
from scipy.constants import hbar
temp *= ev2j
E = eigs * ev2j # Eigenvalues in J
v = 5.2e3 # Velocity in m/s
rho = 5.31e3 # Mass density kg/m^3
ms = .7 * me #effective mass tensor in kg
D_ac = 7 * ev2j # Acoustic deformation potential in J
return (2*ms)**1.5*(D_ac**2)*np.sqrt(E)*temp/(2*np.pi*rho*(hbar**2*v)**2)
# Create the TauModel object
acoustic_tau = TauModel(function=acoustic_model)
# Load the temperatures and corresponding chemical potentials
fname = 'doping_n%s.dat'%np.abs(doping)
temp = np.loadtxt('output/%s'%fname, usecols=(0,))
mu = np.loadtxt('output/%s'%fname, usecols=(1,))
# Define the desired scattering channels, 1 user-defined and 3 built-in.
channels = [acoustic_tau, 'polar_optical', 'impurity', 'polar_acoustic']
# Define quantities required for each built-in TauModel
tau_params = {'doping_conc':-3.5e17, 'D_ac':7., 'rho':5.31e3,
'a':5.653e-10, 'nI':3.5e17, 'eps_inf':11.6, 'eps_0':13.5,
'v':5.2e3, 'Zi':1, 'hwlo':[0.03536], 'D_op':3e10, 'Zf':6,
'piezo':0.16, 'ms':0.7}
# Compute the transport properties for each temperature and chemical potential
rho = []
for t,m in zip(temp,mu):
if paoflow.rank == 0:
print('\nTemp, Mu: %f, %f'%(t,m))
# Update the Fermi energy in the parameters for scattering models
tau_params['Ef'] = abs(m)
paoflow.transport(tmin=t, tmax=t, nt=1, emin=m, emax=m, ne=1, scattering_channels=channels,
tau_dict=tau_params, save_tensors=True, write_to_file=False)
# Average the diagonal componenets of sigma
sigma = np.sum([sig for sig in np.diag(arrays['sigma'][:,:,0])])/3
rho.append(1e2/sigma)
# Write the sigmas
if paoflow.rank == 0:
with open('output/rho_rta_n3.5e17.dat' ,'w') as rho_file:
for i,t in enumerate(temp):
rho_file.write('%8.2f %9.5e\n'%(t,rho[i]))
paoflow.finish_execution()
def main():
model = {'label': 'graphene2', 't': -1.0, 'delta': -0.2}
paoflow = PAOFLOW.PAOFLOW(model=model,
outputdir='./graphene2',
verbose=True)
arry, attr = paoflow.data_controller.data_dicts()
path = 'G-M-K-G'
special_points = {
'G': [0.0, 0.0, 0.0],
'K': [2.0 / 3.0, 1.0 / 3.0, 0.0],
'M': [1.0 / 2.0, 0.0 / 2.0, 0.0]
}
paoflow.bands(ibrav=0,
nk=401,
band_path=path,
high_sym_points=special_points)
kcenter = np.array([1.0 / 3.0, 2.0 / 3.0, 0.0])
kradius = 0.05
paoflow.berry_phase(kspace_method='circle',
nk1=51,
kradius=kradius,
kcenter=kcenter,
sub=[0],
closed=True,
method='berry',
fname='circle_berry_phase_0')
circle_phase_0 = attr['berry_phase']
paoflow.berry_phase(kspace_method='circle',
nk1=51,
kradius=kradius,
kcenter=kcenter,
sub=[1],
closed=True,
method='berry',
fname='circle_berry_phase_1')
circle_phase_1 = attr['berry_phase']
paoflow.berry_phase(kspace_method='circle',
nk1=51,
kradius=kradius,
kcenter=kcenter,
sub=[0, 1],
closed=True,
method='berry',
fname='circle_berry_phase_01')
circle_phase_01 = attr['berry_phase']
print()
print("Berry phase along circle with radius: ", kradius)
print(" centered at k-point: ", kcenter)
print(" for band 0 equals : ", circle_phase_0)
print(" for band 1 equals : ", circle_phase_1)
print(" for both bands equals: ", circle_phase_01)
print()
klength = 0.1
paoflow.berry_phase(
kspace_method='square',
nk1=51,
nk2=51,
kxlim=[kcenter[0] - klength / 2, kcenter[0] + klength / 2],
kylim=[kcenter[1] - klength / 2, kcenter[1] + klength / 2],
sub=[0],
method='berry',
fname='square_berry_phase_0')
square_flux_0 = attr['berry_flux']
paoflow.berry_phase(
kspace_method='square',
nk1=51,
nk2=51,
kxlim=[kcenter[0] - klength / 2, kcenter[0] + klength / 2],
kylim=[kcenter[1] - klength / 2, kcenter[1] + klength / 2],
sub=[1],
method='berry',
fname='square_berry_phase_1')
square_flux_1 = attr['berry_flux']
paoflow.berry_phase(
kspace_method='square',
nk1=51,
nk2=51,
kxlim=[kcenter[0] - klength / 2, kcenter[0] + klength / 2],
kylim=[kcenter[1] - klength / 2, kcenter[1] + klength / 2],
sub=[0, 1],
method='berry',
fname='square_berry_phase_01')
square_flux_01 = attr['berry_flux']
print()
print("Berry flux on square patch with length: ", klength)
print(" centered at k-point: ", kcenter)
print(" for band 0 equals : ", square_flux_0)
print(" for band 1 equals : ", square_flux_1)
print(" for both bands equals: ", square_flux_01)
print()
nk1 = 51
nk2 = 51
berry = np.genfromtxt('graphene2/square_berry_phase_0.dat')
berry = berry.reshape((nk1, nk2, 3), order='F')
kgrid = np.genfromtxt('graphene2/square_berry_phase_0_kgrid_corners.dat')
kgrid = kgrid.reshape((nk1 + 1, nk2 + 1, 2), order='F')
fig, ax = plt.subplots(figsize=(5, 5))
ax.pcolormesh(kgrid[:, :, 0],
kgrid[:, :, 1],
berry[:, :, 2],
shading='flat',
rasterized=True,
cmap='viridis_r')
ax.set_xlabel(r'$k_x$', fontsize=18)
ax.set_ylabel(r'$k_y$', fontsize=18)
fig.tight_layout()
fig.savefig('graphene2/berry_phase_k.pdf', bbox_inches='tight')
paoflow.finish_execution()
def main():
argc = len(argv)
arg1 = ('./' if argc < 2 else argv[1])
arg2 = ('inputfile.xml' if argc < 3 else argv[2])
arg3 = argv[3]
# Start PAOFLOW with an inputfile in the current directory
#
# PAOFLOW will us data attributes read from
# inputfile.xml for the following calculations
paoflow = PAOFLOW.PAOFLOW(acbn0=arg3,
workpath=arg1,
inputfile=arg2,
verbose=True,
outputdir="")
# Get dictionary containers with the
# attributes and arrays read from inputfiles
arry, attr = paoflow.data_controller.data_dicts()
paoflow.projectability()
paoflow.pao_hamiltonian(expand_wedge=attr['expand_wedge'],
thresh=attr['symm_thresh'],
symmetrize=attr['symmetrize'],
max_iter=attr['symm_max_iter'])
if attr['write2file']:
paoflow.write2file()
paoflow.add_external_fields()
if attr['writez2pack']:
paoflow.z2_pack(fname='z2pack_hamiltonian.dat')
if attr['do_bands'] or attr['band_topology']:
paoflow.bands(ibrav=int(attr["ibrav"]))
if attr['spintexture'] or attr['spin_Hall']:
paoflow.spin_operator(spin_orbit=attr['do_spin_orbit'])
if attr['band_topology'] and not attr['onedim']:
paoflow.topology()
elif attr['onedim']:
print('1D Band topology not supported with the PAOFLOW class')
if attr['double_grid']:
paoflow.interpolated_hamiltonian(nfft1=attr['nfft1'],
nfft2=attr['nfft2'],
nfft3=attr['nfft3'])
paoflow.pao_eigh()
if attr['fermisurf']:
paoflow.fermi_surface()
if attr['spintexture']:
paoflow.spin_texture()
paoflow.gradient_and_momenta(band_curvature=attr["carrier_conc"])
if attr['smearing'] is not None:
paoflow.adaptive_smearing()
if attr['do_dos'] or attr['do_pdos']:
paoflow.dos(do_dos=attr['do_dos'],
do_pdos=attr['do_pdos'],
emin=attr['emin'],
emax=attr['emax'])
if attr['spin_Hall']:
paoflow.spin_Hall(do_ac=attr['ac_cond_spin'],
emin=attr['eminSH'],
emax=attr['emaxSH'],
s_tensor=arry['s_tensor'])
if attr['Berry']:
paoflow.anomalous_Hall(do_ac=attr['ac_cond_Berry'],
emin=attr['eminAH'],
emax=attr['emaxSH'],
a_tensor=arry['a_tensor'])
if attr['Boltzmann']:
paoflow.transport(tmin=attr['tmin'],
tmax=attr['tmax'],
tstep=attr['tstep'],
emin=attr['emin'],
emax=attr['emax'],
ne=attr['ne'],
t_tensor=arry['t_tensor'],
carrier_conc=attr["carrier_conc"])
if attr['epsilon']:
paoflow.dielectric_tensor(metal=attr['metal'],
emin=attr['epsmin'],
emax=attr['epsmax'],
ne=attr['ne'],
d_tensor=arry['d_tensor'])
# Print the total execution time and request
# desired quantites for further processing
paoflow.finish_execution()